Strong solution for polymeric fluid-structure interaction with small initial acceleration

TL;DR

The paper addresses a fully coupled 3D-3D-2D fluid–structure interaction problem for a polymeric Oldroyd-B solvent without centre-of-mass diffusion. It develops a high-regularity framework by decoupling the solute (tensor T) from the solvent–structure subsystem, establishing a moving-domain Stokes maximal-regularity theory to control the fluid–shell pair, and solving the solute subproblem via characteristics after a regularity-preserving transformation. A Banach fixed-point argument then reconciles the subproblems to yield a unique local strong solution of the fully coupled system under a small initial-acceleration condition, accompanied by detailed high-order a priori estimates. The work also provides a new moving-domain maximal-regularity result for the Stokes problem with nontrivial boundary data, contributing a robust analytical tool for 3D-3D-2D polymeric-FSI analyses with arbitrary reference configurations.

Abstract

We consider the problem of a 3D-3D-2D mutually coupled solute-solvent-structure three-states system. This describes the interaction of a flexible structure with a polymeric fluid of classical Oldroyd-B type without centre-of-mass diffusion. We construct a unique higher-order regularity notion of a strong solution for the system by decoupling the solute from the solvent-structure subsystem, solving the decoupled system individually, and glueing the solutions through a fixed-point argument. As a requirement for the construction, we rely on a maximal regularity result for the Stokes problem on moving domains with non-trivial boundary conditions; a result that is also of independent interest.

Theorems & Definitions (16)

• Definition 1.1: Strong solution
• Theorem 1.2
• Definition 1.3: Strong solution
• Theorem 1.4
• Theorem 3.1
• Theorem 3.2
• Remark 3.3
• Proposition 3.4
• Remark 3.5
• proof : Proof of Theorem \ref{['thm:stokeInhom']}